LMFDB - Embedded newform 25.7.c.c.18.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,7,Mod(7,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.75135209050$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{201})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 101x^{2} + 2500 $ x^4 + 101*x^2 + 2500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.2
Root			$-7.58872i$ of defining polynomial
Character	$\chi$	$=$	25.18
Dual form			25.7.c.c.7.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.58872 - 9.58872i) q^{2} +(-14.5887 - 14.5887i) q^{3} -119.887i q^{4} -279.774 q^{6} +(-59.5240 + 59.5240i) q^{7} +(-535.887 - 535.887i) q^{8} -303.338i q^{9} +O(q^{10})$	\(q+(9.58872 - 9.58872i) q^{2} +(-14.5887 - 14.5887i) q^{3} -119.887i q^{4} -279.774 q^{6} +(-59.5240 + 59.5240i) q^{7} +(-535.887 - 535.887i) q^{8} -303.338i q^{9} +800.309 q^{11} +(-1749.00 + 1749.00i) q^{12} +(459.889 + 459.889i) q^{13} +1141.52i q^{14} -2604.17 q^{16} +(2989.15 - 2989.15i) q^{17} +(-2908.63 - 2908.63i) q^{18} -6971.14i q^{19} +1736.76 q^{21} +(7673.94 - 7673.94i) q^{22} +(12013.8 + 12013.8i) q^{23} +15635.8i q^{24} +8819.50 q^{26} +(-15060.5 + 15060.5i) q^{27} +(7136.17 + 7136.17i) q^{28} +26318.7i q^{29} +16163.1 q^{31} +(9326.16 - 9326.16i) q^{32} +(-11675.5 - 11675.5i) q^{33} -57324.3i q^{34} -36366.4 q^{36} +(-16894.9 + 16894.9i) q^{37} +(-66844.4 - 66844.4i) q^{38} -13418.4i q^{39} -124725. q^{41} +(16653.3 - 16653.3i) q^{42} +(29630.9 + 29630.9i) q^{43} -95946.8i q^{44} +230394. q^{46} +(-35714.9 + 35714.9i) q^{47} +(37991.5 + 37991.5i) q^{48} +110563. i q^{49} -87215.7 q^{51} +(55134.8 - 55134.8i) q^{52} +(-45590.3 - 45590.3i) q^{53} +288822. i q^{54} +63796.3 q^{56} +(-101700. + 101700. i) q^{57} +(252363. + 252363. i) q^{58} -5231.18i q^{59} +20085.9 q^{61} +(154983. - 154983. i) q^{62} +(18055.9 + 18055.9i) q^{63} -345518. i q^{64} -223906. q^{66} +(228348. - 228348. i) q^{67} +(-358361. - 358361. i) q^{68} -350532. i q^{69} +471094. q^{71} +(-162555. + 162555. i) q^{72} +(24258.7 + 24258.7i) q^{73} +324002. i q^{74} -835751. q^{76} +(-47637.6 + 47637.6i) q^{77} +(-128665. - 128665. i) q^{78} +476823. i q^{79} +218293. q^{81} +(-1.19595e6 + 1.19595e6i) q^{82} +(296628. + 296628. i) q^{83} -208215. i q^{84} +568245. q^{86} +(383957. - 383957. i) q^{87} +(-428875. - 428875. i) q^{88} -834303. i q^{89} -54748.9 q^{91} +(1.44030e6 - 1.44030e6i) q^{92} +(-235799. - 235799. i) q^{93} +684921. i q^{94} -272113. q^{96} +(60336.2 - 60336.2i) q^{97} +(1.06016e6 + 1.06016e6i) q^{98} -242764. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8}+O(q^{10}) $ 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8	$ 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8} - 1052 q^{11} - 3480 q^{12} - 1960 q^{13} - 776 q^{16} + 3280 q^{17} + 870 q^{18} + 3828 q^{21} + 27520 q^{22} + 39010 q^{23} + 44068 q^{26} - 31320 q^{27} + 4840 q^{28} - 33172 q^{31} + 48760 q^{32} - 22260 q^{33} - 40836 q^{36} - 146860 q^{37} - 218040 q^{38} - 213932 q^{41} + 31680 q^{42} + 72050 q^{43} + 323288 q^{46} - 830 q^{47} + 74160 q^{48} - 172212 q^{51} + 173300 q^{52} + 29620 q^{53} + 467280 q^{56} - 195840 q^{57} + 554640 q^{58} - 111052 q^{61} + 610520 q^{62} + 350130 q^{63} - 457824 q^{66} + 146930 q^{67} - 775780 q^{68} + 1310188 q^{71} - 899460 q^{72} - 553540 q^{73} - 2073840 q^{76} + 476300 q^{77} - 268200 q^{78} - 624816 q^{81} - 2554880 q^{82} - 536870 q^{83} + 1019128 q^{86} + 763440 q^{87} + 187680 q^{88} + 1131548 q^{91} + 2552680 q^{92} - 444660 q^{93} - 568992 q^{96} + 59420 q^{97} + 1892810 q^{98}+O(q^{100}) $ 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8 - 1052 * q^11 - 3480 * q^12 - 1960 * q^13 - 776 * q^16 + 3280 * q^17 + 870 * q^18 + 3828 * q^21 + 27520 * q^22 + 39010 * q^23 + 44068 * q^26 - 31320 * q^27 + 4840 * q^28 - 33172 * q^31 + 48760 * q^32 - 22260 * q^33 - 40836 * q^36 - 146860 * q^37 - 218040 * q^38 - 213932 * q^41 + 31680 * q^42 + 72050 * q^43 + 323288 * q^46 - 830 * q^47 + 74160 * q^48 - 172212 * q^51 + 173300 * q^52 + 29620 * q^53 + 467280 * q^56 - 195840 * q^57 + 554640 * q^58 - 111052 * q^61 + 610520 * q^62 + 350130 * q^63 - 457824 * q^66 + 146930 * q^67 - 775780 * q^68 + 1310188 * q^71 - 899460 * q^72 - 553540 * q^73 - 2073840 * q^76 + 476300 * q^77 - 268200 * q^78 - 624816 * q^81 - 2554880 * q^82 - 536870 * q^83 + 1019128 * q^86 + 763440 * q^87 + 187680 * q^88 + 1131548 * q^91 + 2552680 * q^92 - 444660 * q^93 - 568992 * q^96 + 59420 * q^97 + 1892810 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	9.58872	−	9.58872i	1.19859	−	1.19859i	0.224002	−	0.974589i	$-0.428088\pi$
$2$	9.58872	−	9.58872i	1.19859	−	1.19859i	0.974589	−	0.224002i	$-0.0719121\pi$
$3$	−14.5887	−	14.5887i	−0.540323	−	0.540323i	0.383301	−	0.923624i	$-0.374787\pi$
$3$	−14.5887	−	14.5887i	−0.540323	−	0.540323i	−0.923624	+	0.383301i	$0.874787\pi$
$4$		−	119.887i		−	1.87324i
$5$		0			0
$5$		0			0
$6$	−279.774			−1.29525
$7$	−59.5240	+	59.5240i	−0.173539	+	0.173539i	−0.788533	−	0.614993i	$-0.789159\pi$
$7$	−59.5240	+	59.5240i	−0.173539	+	0.173539i	0.614993	+	0.788533i	$0.289159\pi$
$8$	−535.887	−	535.887i	−1.04665	−	1.04665i
$9$		−	303.338i		−	0.416102i
$10$		0			0
$11$	800.309			0.601284			0.300642	−	0.953737i	$-0.402799\pi$
$11$	800.309			0.601284			0.300642	+	0.953737i	$0.402799\pi$
$12$	−1749.00	+	1749.00i	−1.01215	+	1.01215i
$13$	459.889	+	459.889i	0.209326	+	0.209326i	0.803981	−	0.594655i	$-0.202711\pi$
$13$	459.889	+	459.889i	0.209326	+	0.209326i	−0.594655	+	0.803981i	$0.702711\pi$
$14$			1141.52i			0.416006i
$15$		0			0
$16$	−2604.17			−0.635783
$17$	2989.15	−	2989.15i	0.608416	−	0.608416i	−0.334116	−	0.942532i	$-0.608438\pi$
$17$	2989.15	−	2989.15i	0.608416	−	0.608416i	0.942532	+	0.334116i	$0.108438\pi$
$18$	−2908.63	−	2908.63i	−0.498736	−	0.498736i
$19$		−	6971.14i		−	1.01635i	−0.861254	−	0.508175i	$-0.830320\pi$
$19$		−	6971.14i		−	1.01635i	0.861254	−	0.508175i	$-0.169680\pi$
$20$		0			0
$21$	1736.76			0.187535
$22$	7673.94	−	7673.94i	0.720693	−	0.720693i
$23$	12013.8	+	12013.8i	0.987409	+	0.987409i	0.999922	−	0.0125129i	$-0.00398309\pi$
$23$	12013.8	+	12013.8i	0.987409	+	0.987409i	−0.0125129	+	0.999922i	$0.503983\pi$
$24$			15635.8i			1.13106i
$25$		0			0
$26$	8819.50			0.501792
$27$	−15060.5	+	15060.5i	−0.765153	+	0.765153i
$28$	7136.17	+	7136.17i	0.325081	+	0.325081i
$29$			26318.7i			1.07912i	0.841946	+	0.539562i	$0.181410\pi$
$29$			26318.7i			1.07912i	−0.841946	+	0.539562i	$0.818590\pi$
$30$		0			0
$31$	16163.1			0.542550			0.271275	−	0.962502i	$-0.412555\pi$
$31$	16163.1			0.542550			0.271275	+	0.962502i	$0.412555\pi$
$32$	9326.16	−	9326.16i	0.284612	−	0.284612i
$33$	−11675.5	−	11675.5i	−0.324887	−	0.324887i
$34$		−	57324.3i		−	1.45848i
$35$		0			0
$36$	−36366.4			−0.779458
$37$	−16894.9	+	16894.9i	−0.333543	+	0.333543i	−0.853930	−	0.520388i	$-0.825787\pi$
$37$	−16894.9	+	16894.9i	−0.333543	+	0.333543i	0.520388	+	0.853930i	$0.325787\pi$
$38$	−66844.4	−	66844.4i	−1.21819	−	1.21819i
$39$		−	13418.4i		−	0.226207i
$40$		0			0
$41$	−124725.			−1.80968			−0.904838	−	0.425756i	$-0.860008\pi$
$41$	−124725.			−1.80968			−0.904838	+	0.425756i	$0.860008\pi$
$42$	16653.3	−	16653.3i	0.224777	−	0.224777i
$43$	29630.9	+	29630.9i	0.372683	+	0.372683i	0.868454	−	0.495770i	$-0.165114\pi$
$43$	29630.9	+	29630.9i	0.372683	+	0.372683i	−0.495770	+	0.868454i	$0.665114\pi$
$44$		−	95946.8i		−	1.12635i
$45$		0			0
$46$	230394.			2.36700
$47$	−35714.9	+	35714.9i	−0.343998	+	0.343998i	−0.857868	−	0.513870i	$-0.828211\pi$
$47$	−35714.9	+	35714.9i	−0.343998	+	0.343998i	0.513870	+	0.857868i	$0.328211\pi$
$48$	37991.5	+	37991.5i	0.343528	+	0.343528i
$49$			110563.i			0.939768i
$50$		0			0
$51$	−87215.7			−0.657483
$52$	55134.8	−	55134.8i	0.392117	−	0.392117i
$53$	−45590.3	−	45590.3i	−0.306228	−	0.306228i	0.537216	−	0.843444i	$-0.319476\pi$
$53$	−45590.3	−	45590.3i	−0.306228	−	0.306228i	−0.843444	+	0.537216i	$0.819476\pi$
$54$			288822.i			1.83421i
$55$		0			0
$56$	63796.3			0.363272
$57$	−101700.	+	101700.i	−0.549157	+	0.549157i
$58$	252363.	+	252363.i	1.29343	+	1.29343i
$59$		−	5231.18i		−	0.0254709i	−0.999919	−	0.0127354i	$-0.995946\pi$
$59$		−	5231.18i		−	0.0254709i	0.999919	−	0.0127354i	$-0.00405392\pi$
$60$		0			0
$61$	20085.9			0.0884915			0.0442457	−	0.999021i	$-0.485912\pi$
$61$	20085.9			0.0884915			0.0442457	+	0.999021i	$0.485912\pi$
$62$	154983.	−	154983.i	0.650295	−	0.650295i
$63$	18055.9	+	18055.9i	0.0722101	+	0.0722101i
$64$		−	345518.i		−	1.31805i
$65$		0			0
$66$	−223906.			−0.778814
$67$	228348.	−	228348.i	0.759228	−	0.759228i	−0.216954	−	0.976182i	$-0.569612\pi$
$67$	228348.	−	228348.i	0.759228	−	0.759228i	0.976182	+	0.216954i	$0.0696120\pi$
$68$	−358361.	−	358361.i	−1.13971	−	1.13971i
$69$		−	350532.i		−	1.06704i
$70$		0			0
$71$	471094.			1.31623			0.658116	−	0.752917i	$-0.271354\pi$
$71$	471094.			1.31623			0.658116	+	0.752917i	$0.271354\pi$
$72$	−162555.	+	162555.i	−0.435515	+	0.435515i
$73$	24258.7	+	24258.7i	0.0623589	+	0.0623589i	0.737598	−	0.675240i	$-0.235960\pi$
$73$	24258.7	+	24258.7i	0.0623589	+	0.0623589i	−0.675240	+	0.737598i	$0.735960\pi$
$74$			324002.i			0.799562i
$75$		0			0
$76$	−835751.			−1.90387
$77$	−47637.6	+	47637.6i	−0.104346	+	0.104346i
$78$	−128665.	−	128665.i	−0.271130	−	0.271130i
$79$			476823.i			0.967109i	0.875314	+	0.483555i	$0.160655\pi$
$79$			476823.i			0.967109i	−0.875314	+	0.483555i	$0.839345\pi$
$80$		0			0
$81$	218293.			0.410757
$82$	−1.19595e6	+	1.19595e6i	−2.16906	+	2.16906i
$83$	296628.	+	296628.i	0.518774	+	0.518774i	0.917200	−	0.398427i	$-0.130444\pi$
$83$	296628.	+	296628.i	0.518774	+	0.518774i	−0.398427	+	0.917200i	$0.630444\pi$
$84$		−	208215.i		−	0.351297i
$85$		0			0
$86$	568245.			0.893389
$87$	383957.	−	383957.i	0.583075	−	0.583075i
$88$	−428875.	−	428875.i	−0.629336	−	0.629336i
$89$		−	834303.i		−	1.18346i	−0.806136	−	0.591730i	$-0.798445\pi$
$89$		−	834303.i		−	1.18346i	0.806136	−	0.591730i	$-0.201555\pi$
$90$		0			0
$91$	−54748.9			−0.0726526
$92$	1.44030e6	−	1.44030e6i	1.84965	−	1.84965i
$93$	−235799.	−	235799.i	−0.293152	−	0.293152i
$94$			684921.i			0.824626i
$95$		0			0
$96$	−272113.			−0.307565
$97$	60336.2	−	60336.2i	0.0661094	−	0.0661094i	−0.673279	−	0.739388i	$-0.735115\pi$
$97$	60336.2	−	60336.2i	0.0661094	−	0.0661094i	0.739388	+	0.673279i	$0.235115\pi$
$98$	1.06016e6	+	1.06016e6i	1.12640	+	1.12640i
$99$		−	242764.i		−	0.250195i
$100$		0			0
$101$	−91011.0			−0.0883343			−0.0441672	−	0.999024i	$-0.514063\pi$
$101$	−91011.0			−0.0883343			−0.0441672	+	0.999024i	$0.514063\pi$
$102$	−836288.	+	836288.i	−0.788053	+	0.788053i
$103$	−635957.	−	635957.i	−0.581991	−	0.581991i	0.353459	−	0.935450i	$-0.385005\pi$
$103$	−635957.	−	635957.i	−0.581991	−	0.581991i	−0.935450	+	0.353459i	$0.885005\pi$
$104$		−	492897.i		−	0.438184i
$105$		0			0
$106$	−874305.			−0.734084
$107$	277680.	−	277680.i	0.226670	−	0.226670i	−0.584630	−	0.811300i	$-0.698760\pi$
$107$	277680.	−	277680.i	0.226670	−	0.226670i	0.811300	+	0.584630i	$0.198760\pi$
$108$	1.80556e6	+	1.80556e6i	1.43331	+	1.43331i
$109$			981017.i			0.757525i	0.925494	+	0.378763i	$0.123650\pi$
$109$			981017.i			0.757525i	−0.925494	+	0.378763i	$0.876350\pi$
$110$		0			0
$111$	492951.			0.360441
$112$	155010.	−	155010.i	0.110333	−	0.110333i
$113$	−1.44645e6	−	1.44645e6i	−1.00246	−	1.00246i	−0.999997	−	0.00246631i	$-0.999215\pi$
$113$	−1.44645e6	−	1.44645e6i	−1.00246	−	1.00246i	−0.00246631	−	0.999997i	$-0.500785\pi$
$114$			1.95035e6i			1.31643i
$115$		0			0
$116$	3.15528e6			2.02145
$117$	139502.	−	139502.i	0.0871009	−	0.0871009i
$118$	−50160.3	−	50160.3i	−0.0305291	−	0.0305291i
$119$			355853.i			0.211169i
$120$		0			0
$121$	−1.13107e6			−0.638458
$122$	192598.	−	192598.i	0.106065	−	0.106065i
$123$	1.81957e6	+	1.81957e6i	0.977810	+	0.977810i
$124$		−	1.93775e6i		−	1.01632i
$125$		0			0
$126$	346266.			0.173101
$127$	−1.78869e6	+	1.78869e6i	−0.873220	+	0.873220i	−0.992822	−	0.119602i	$-0.961838\pi$
$127$	−1.78869e6	+	1.78869e6i	−0.873220	+	0.873220i	0.119602	+	0.992822i	$0.461838\pi$
$128$	−2.71621e6	−	2.71621e6i	−1.29519	−	1.29519i
$129$		−	864555.i		−	0.402739i
$130$		0			0
$131$	−3.08768e6			−1.37347			−0.686735	−	0.726908i	$-0.740957\pi$
$131$	−3.08768e6			−1.37347			−0.686735	+	0.726908i	$0.740957\pi$
$132$	−1.39974e6	+	1.39974e6i	−0.608591	+	0.608591i
$133$	414951.	+	414951.i	0.176377	+	0.176377i
$134$		−	4.37913e6i		−	1.82001i
$135$		0			0
$136$	−3.20369e6			−1.27360
$137$	118847.	−	118847.i	0.0462197	−	0.0462197i	−0.683619	−	0.729839i	$-0.739595\pi$
$137$	118847.	−	118847.i	0.0462197	−	0.0462197i	0.729839	+	0.683619i	$0.239595\pi$
$138$	−3.36116e6	−	3.36116e6i	−1.27894	−	1.27894i
$139$			2.22764e6i			0.829468i	0.909943	+	0.414734i	$0.136125\pi$
$139$			2.22764e6i			0.829468i	−0.909943	+	0.414734i	$0.863875\pi$
$140$		0			0
$141$	1.04207e6			0.371740
$142$	4.51719e6	−	4.51719e6i	1.57762	−	1.57762i
$143$	368053.	+	368053.i	0.125864	+	0.125864i
$144$			789943.i			0.264550i
$145$		0			0
$146$	465219.			0.149486
$147$	1.61297e6	−	1.61297e6i	0.507778	−	0.507778i
$148$	2.02549e6	+	2.02549e6i	0.624805	+	0.624805i
$149$		−	1.55027e6i		−	0.468649i	−0.972158	−	0.234325i	$-0.924712\pi$
$149$		−	1.55027e6i		−	0.468649i	0.972158	−	0.234325i	$-0.0752879\pi$
$150$		0			0
$151$	6.27210e6			1.82172			0.910860	−	0.412715i	$-0.135419\pi$
$151$	6.27210e6			1.82172			0.910860	+	0.412715i	$0.135419\pi$
$152$	−3.73575e6	+	3.73575e6i	−1.06377	+	1.06377i
$153$	−906723.	−	906723.i	−0.253163	−	0.253163i
$154$			913568.i			0.250137i
$155$		0			0
$156$	−1.60869e6			−0.423740
$157$	−4.24526e6	+	4.24526e6i	−1.09700	+	1.09700i	−0.102235	+	0.994760i	$0.532599\pi$
$157$	−4.24526e6	+	4.24526e6i	−1.09700	+	1.09700i	−0.994760	+	0.102235i	$0.967401\pi$
$158$	4.57212e6	+	4.57212e6i	1.15917	+	1.15917i
$159$			1.33021e6i			0.330924i
$160$		0			0
$161$	−1.43022e6			−0.342709
$162$	2.09315e6	−	2.09315e6i	0.492330	−	0.492330i
$163$	4.99321e6	+	4.99321e6i	1.15297	+	1.15297i	0.985955	+	0.167013i	$0.0534122\pi$
$163$	4.99321e6	+	4.99321e6i	1.15297	+	1.15297i	0.167013	+	0.985955i	$0.446588\pi$
$164$			1.49529e7i			3.38995i
$165$		0			0
$166$	5.68857e6			1.24359
$167$	2.10663e6	−	2.10663e6i	0.452314	−	0.452314i	−0.443808	−	0.896122i	$-0.646373\pi$
$167$	2.10663e6	−	2.10663e6i	0.452314	−	0.452314i	0.896122	+	0.443808i	$0.146373\pi$
$168$	−930707.	−	930707.i	−0.196284	−	0.196284i
$169$		−	4.40381e6i		−	0.912365i
$170$		0			0
$171$	−2.11462e6			−0.422905
$172$	3.55237e6	−	3.55237e6i	0.698124	−	0.698124i
$173$	−1.97319e6	−	1.97319e6i	−0.381093	−	0.381093i	0.490403	−	0.871496i	$-0.336850\pi$
$173$	−1.97319e6	−	1.97319e6i	−0.381093	−	0.381093i	−0.871496	+	0.490403i	$0.836850\pi$
$174$		−	7.36331e6i		−	1.39774i
$175$		0			0
$176$	−2.08414e6			−0.382286
$177$	−76316.2	+	76316.2i	−0.0137625	+	0.0137625i
$178$	−7.99990e6	−	7.99990e6i	−1.41848	−	1.41848i
$179$			1.84747e6i			0.322121i	0.986945	+	0.161061i	$0.0514915\pi$
$179$			1.84747e6i			0.322121i	−0.986945	+	0.161061i	$0.948509\pi$
$180$		0			0
$181$	−2.94668e6			−0.496932			−0.248466	−	0.968641i	$-0.579926\pi$
$181$	−2.94668e6			−0.496932			−0.248466	+	0.968641i	$0.579926\pi$
$182$	−524972.	+	524972.i	−0.0870807	+	0.0870807i
$183$	−293027.	−	293027.i	−0.0478140	−	0.0478140i
$184$		−	1.28761e7i		−	2.06695i
$185$		0			0
$186$	−4.52202e6			−0.702739
$187$	2.39224e6	−	2.39224e6i	0.365831	−	0.365831i
$188$	4.28176e6	+	4.28176e6i	0.644390	+	0.644390i
$189$		−	1.79292e6i		−	0.265568i
$190$		0			0
$191$	−2.03592e6			−0.292187			−0.146094	−	0.989271i	$-0.546670\pi$
$191$	−2.03592e6			−0.292187			−0.146094	+	0.989271i	$0.546670\pi$
$192$	−5.04067e6	+	5.04067e6i	−0.712172	+	0.712172i
$193$	−321544.	−	321544.i	−0.0447269	−	0.0447269i	0.684390	−	0.729116i	$-0.260069\pi$
$193$	−321544.	−	321544.i	−0.0447269	−	0.0447269i	−0.729116	+	0.684390i	$0.760069\pi$
$194$		−	1.15710e6i		−	0.158476i
$195$		0			0
$196$	1.32551e7			1.76041
$197$	−5.21092e6	+	5.21092e6i	−0.681578	+	0.681578i	−0.960356	−	0.278778i	$-0.910071\pi$
$197$	−5.21092e6	+	5.21092e6i	−0.681578	+	0.681578i	0.278778	+	0.960356i	$0.410071\pi$
$198$	−2.32780e6	−	2.32780e6i	−0.299882	−	0.299882i
$199$			9.26912e6i			1.17620i	0.808790	+	0.588098i	$0.200123\pi$
$199$			9.26912e6i			1.17620i	−0.808790	+	0.588098i	$0.799877\pi$
$200$		0			0
$201$	−6.66261e6			−0.820457
$202$	−872679.	+	872679.i	−0.105877	+	0.105877i
$203$	−1.56660e6	−	1.56660e6i	−0.187271	−	0.187271i
$204$			1.04561e7i			1.23162i
$205$		0			0
$206$	−1.21960e7			−1.39514
$207$	3.64425e6	−	3.64425e6i	0.410863	−	0.410863i
$208$	−1.19763e6	−	1.19763e6i	−0.133086	−	0.133086i
$209$		−	5.57907e6i		−	0.611115i
$210$		0			0
$211$	1.13498e7			1.20820			0.604101	−	0.796907i	$-0.293532\pi$
$211$	1.13498e7			1.20820			0.604101	+	0.796907i	$0.293532\pi$
$212$	−5.46569e6	+	5.46569e6i	−0.573638	+	0.573638i
$213$	−6.87265e6	−	6.87265e6i	−0.711190	−	0.711190i
$214$		−	5.32520e6i		−	0.543369i
$215$		0			0
$216$	1.61415e7			1.60170
$217$	−962093.	+	962093.i	−0.0941538	+	0.0941538i
$218$	9.40671e6	+	9.40671e6i	0.907963	+	0.907963i
$219$		−	707806.i		−	0.0673879i
$220$		0			0
$221$	2.74935e6			0.254715
$222$	4.72677e6	−	4.72677e6i	0.432022	−	0.432022i
$223$	2.22688e6	+	2.22688e6i	0.200809	+	0.200809i	0.800346	−	0.599538i	$-0.204649\pi$
$223$	2.22688e6	+	2.22688e6i	0.200809	+	0.200809i	−0.599538	+	0.800346i	$0.704649\pi$
$224$			1.11026e6i			0.0987827i
$225$		0			0
$226$	−2.77392e7			−2.40309
$227$	134399.	−	134399.i	0.0114899	−	0.0114899i	−0.701338	−	0.712828i	$-0.747414\pi$
$227$	134399.	−	134399.i	0.0114899	−	0.0114899i	0.712828	+	0.701338i	$0.247414\pi$
$228$	1.21925e7	+	1.21925e7i	1.02870	+	1.02870i
$229$			1.63704e7i			1.36318i	0.731735	+	0.681589i	$0.238711\pi$
$229$			1.63704e7i			1.36318i	−0.731735	+	0.681589i	$0.761289\pi$
$230$		0			0
$231$	1.38994e6			0.112762
$232$	1.41039e7	−	1.41039e7i	1.12947	−	1.12947i
$233$	−1.12976e7	−	1.12976e7i	−0.893137	−	0.893137i	0.101680	−	0.994817i	$-0.467578\pi$
$233$	−1.12976e7	−	1.12976e7i	−0.893137	−	0.893137i	−0.994817	+	0.101680i	$0.967578\pi$
$234$		−	2.67529e6i		−	0.208797i
$235$		0			0
$236$	−627152.			−0.0477130
$237$	6.95623e6	−	6.95623e6i	0.522551	−	0.522551i
$238$	3.41217e6	+	3.41217e6i	0.253105	+	0.253105i
$239$		−	1.90970e7i		−	1.39885i	−0.714705	−	0.699426i	$-0.753439\pi$
$239$		−	1.90970e7i		−	1.39885i	0.714705	−	0.699426i	$-0.246561\pi$
$240$		0			0
$241$	−1.68760e6			−0.120564			−0.0602821	−	0.998181i	$-0.519200\pi$
$241$	−1.68760e6			−0.120564			−0.0602821	+	0.998181i	$0.519200\pi$
$242$	−1.08455e7	+	1.08455e7i	−0.765250	+	0.765250i
$243$	7.79448e6	+	7.79448e6i	0.543211	+	0.543211i
$244$		−	2.40804e6i		−	0.165766i
$245$		0			0
$246$	3.48948e7			2.34399
$247$	3.20595e6	−	3.20595e6i	0.212748	−	0.212748i
$248$	−8.66160e6	−	8.66160e6i	−0.567862	−	0.567862i
$249$		−	8.65485e6i		−	0.560611i
$250$		0			0
$251$	886478.			0.0560592			0.0280296	−	0.999607i	$-0.491077\pi$
$251$	886478.			0.0560592			0.0280296	+	0.999607i	$0.491077\pi$
$252$	2.16467e6	−	2.16467e6i	0.135267	−	0.135267i
$253$	9.61475e6	+	9.61475e6i	0.593713	+	0.593713i
$254$			3.43025e7i			2.09327i
$255$		0			0
$256$	−2.99767e7			−1.78675
$257$	8.52467e6	−	8.52467e6i	0.502202	−	0.502202i	−0.409920	−	0.912122i	$-0.634443\pi$
$257$	8.52467e6	−	8.52467e6i	0.502202	−	0.502202i	0.912122	+	0.409920i	$0.134443\pi$
$258$	−8.28997e6	−	8.28997e6i	−0.482719	−	0.482719i
$259$		−	2.01131e6i		−	0.115766i
$260$		0			0
$261$	7.98348e6			0.449025
$262$	−2.96069e7	+	2.96069e7i	−1.64623	+	1.64623i
$263$	9.22908e6	+	9.22908e6i	0.507331	+	0.507331i	0.913706	−	0.406376i	$-0.133208\pi$
$263$	9.22908e6	+	9.22908e6i	0.507331	+	0.507331i	−0.406376	+	0.913706i	$0.633208\pi$
$264$			1.25135e7i			0.680090i
$265$		0			0
$266$	7.95770e6			0.422807
$267$	−1.21714e7	+	1.21714e7i	−0.639451	+	0.639451i
$268$	−2.73760e7	−	2.73760e7i	−1.42222	−	1.42222i
$269$		−	4.44151e6i		−	0.228178i	−0.993471	−	0.114089i	$-0.963605\pi$
$269$		−	4.44151e6i		−	0.228178i	0.993471	−	0.114089i	$-0.0363949\pi$
$270$		0			0
$271$	5.48744e6			0.275716			0.137858	−	0.990452i	$-0.455978\pi$
$271$	5.48744e6			0.275716			0.137858	+	0.990452i	$0.455978\pi$
$272$	−7.78424e6	+	7.78424e6i	−0.386821	+	0.386821i
$273$	798717.	+	798717.i	0.0392559	+	0.0392559i
$274$		−	2.27918e6i		−	0.110797i
$275$		0			0
$276$	−4.20243e7			−1.99882
$277$	1.03455e7	−	1.03455e7i	0.486756	−	0.486756i	−0.420525	−	0.907281i	$-0.638154\pi$
$277$	1.03455e7	−	1.03455e7i	0.486756	−	0.486756i	0.907281	+	0.420525i	$0.138154\pi$
$278$	2.13602e7	+	2.13602e7i	0.994192	+	0.994192i
$279$		−	4.90289e6i		−	0.225756i
$280$		0			0
$281$	1.06286e7			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$281$	1.06286e7			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$282$	9.99212e6	−	9.99212e6i	0.445564	−	0.445564i
$283$	−2.67853e7	−	2.67853e7i	−1.18178	−	1.18178i	−0.979282	−	0.202501i	$-0.935093\pi$
$283$	−2.67853e7	−	2.67853e7i	−1.18178	−	1.18178i	−0.202501	−	0.979282i	$-0.564907\pi$
$284$		−	5.64781e7i		−	2.46561i
$285$		0			0
$286$	7.05832e6			0.301719
$287$	7.42412e6	−	7.42412e6i	0.314050	−	0.314050i
$288$	−2.82898e6	−	2.82898e6i	−0.118427	−	0.118427i
$289$			6.26754e6i			0.259659i
$290$		0			0
$291$	−1.76046e6			−0.0714409
$292$	2.90830e6	−	2.90830e6i	0.116813	−	0.116813i
$293$	8.76469e6	+	8.76469e6i	0.348445	+	0.348445i	0.859530	−	0.511085i	$-0.170756\pi$
$293$	8.76469e6	+	8.76469e6i	0.348445	+	0.348445i	−0.511085	+	0.859530i	$0.670756\pi$
$294$		−	3.09326e7i		−	1.21724i
$295$		0			0
$296$	1.81076e7			0.698208
$297$	−1.20530e7	+	1.20530e7i	−0.460074	+	0.460074i
$298$	−1.48651e7	−	1.48651e7i	−0.561719	−	0.561719i
$299$			1.10500e7i			0.413380i
$300$		0			0
$301$	−3.52750e6			−0.129350
$302$	6.01414e7	−	6.01414e7i	2.18350	−	2.18350i
$303$	1.32773e6	+	1.32773e6i	0.0477291	+	0.0477291i
$304$			1.81540e7i			0.646178i
$305$		0			0
$306$	−1.73886e7			−0.606878
$307$	−2.94600e7	+	2.94600e7i	−1.01816	+	1.01816i	−0.0183331	+	0.999832i	$0.505836\pi$
$307$	−2.94600e7	+	2.94600e7i	−1.01816	+	1.01816i	−0.999832	+	0.0183331i	$0.994164\pi$
$308$	5.71114e6	+	5.71114e6i	0.195466	+	0.195466i
$309$			1.85556e7i			0.628926i
$310$		0			0
$311$	−5.27556e7			−1.75383			−0.876915	−	0.480645i	$-0.840403\pi$
$311$	−5.27556e7			−1.75383			−0.876915	+	0.480645i	$0.840403\pi$
$312$	−7.19074e6	+	7.19074e6i	−0.236761	+	0.236761i
$313$	3.45882e7	+	3.45882e7i	1.12796	+	1.12796i	0.990508	+	0.137457i	$0.0438928\pi$
$313$	3.45882e7	+	3.45882e7i	1.12796	+	1.12796i	0.137457	+	0.990508i	$0.456107\pi$
$314$			8.14132e7i			2.62970i
$315$		0			0
$316$	5.71649e7			1.81163
$317$	−3.73217e7	+	3.73217e7i	−1.17161	+	1.17161i	−0.189786	+	0.981826i	$0.560779\pi$
$317$	−3.73217e7	+	3.73217e7i	−1.17161	+	1.17161i	−0.981826	+	0.189786i	$0.939221\pi$
$318$	1.27550e7	+	1.27550e7i	0.396642	+	0.396642i
$319$			2.10631e7i			0.648859i
$320$		0			0
$321$	−8.10201e6			−0.244950
$322$	−1.37140e7	+	1.37140e7i	−0.410768	+	0.410768i
$323$	−2.08378e7	−	2.08378e7i	−0.618364	−	0.618364i
$324$		−	2.61706e7i		−	0.769446i
$325$		0			0
$326$	9.57571e7			2.76387
$327$	1.43118e7	−	1.43118e7i	0.409309	−	0.409309i
$328$	6.68384e7	+	6.68384e7i	1.89411	+	1.89411i
$329$		−	4.25179e6i		−	0.119395i
$330$		0			0
$331$	−1.72069e7			−0.474481			−0.237241	−	0.971451i	$-0.576243\pi$
$331$	−1.72069e7			−0.474481			−0.237241	+	0.971451i	$0.576243\pi$
$332$	3.55619e7	−	3.55619e7i	0.971787	−	0.971787i
$333$	5.12488e6	+	5.12488e6i	0.138788	+	0.138788i
$334$		−	4.03999e7i		−	1.08428i
$335$		0			0
$336$	−4.52281e6			−0.119231
$337$	3.84422e7	−	3.84422e7i	1.00443	−	1.00443i	0.00443712	−	0.999990i	$-0.498588\pi$
$337$	3.84422e7	−	3.84422e7i	1.00443	−	1.00443i	0.999990	−	0.00443712i	$-0.00141239\pi$
$338$	−4.22269e7	−	4.22269e7i	−1.09355	−	1.09355i
$339$			4.22038e7i			1.08331i
$340$		0			0
$341$	1.29355e7			0.326226
$342$	−2.02765e7	+	2.02765e7i	−0.506890	+	0.506890i
$343$	−1.35841e7	−	1.35841e7i	−0.336626	−	0.336626i
$344$		−	3.17577e7i		−	0.780141i
$345$		0			0
$346$	−3.78408e7			−0.913549
$347$	−2.41898e7	+	2.41898e7i	−0.578955	+	0.578955i	−0.934615	−	0.355661i	$-0.884256\pi$
$347$	−2.41898e7	+	2.41898e7i	−0.578955	+	0.578955i	0.355661	+	0.934615i	$0.384256\pi$
$348$	−4.60315e7	−	4.60315e7i	−1.09224	−	1.09224i
$349$		−	3.28046e7i		−	0.771718i	−0.922558	−	0.385859i	$-0.873905\pi$
$349$		−	3.28046e7i		−	0.771718i	0.922558	−	0.385859i	$-0.126095\pi$
$350$		0			0
$351$	−1.38523e7			−0.320332
$352$	7.46380e6	−	7.46380e6i	0.171132	−	0.171132i
$353$	−2.11688e7	−	2.11688e7i	−0.481252	−	0.481252i	0.424279	−	0.905531i	$-0.360527\pi$
$353$	−2.11688e7	−	2.11688e7i	−0.481252	−	0.481252i	−0.905531	+	0.424279i	$0.860527\pi$
$354$			1.46355e6i			0.0329912i
$355$		0			0
$356$	−1.00022e8			−2.21690
$357$	5.19143e6	−	5.19143e6i	0.114099	−	0.114099i
$358$	1.77149e7	+	1.77149e7i	0.386091	+	0.386091i
$359$		−	5.98132e7i		−	1.29275i	−0.763021	−	0.646374i	$-0.776285\pi$
$359$		−	5.98132e7i		−	1.29275i	0.763021	−	0.646374i	$-0.223715\pi$
$360$		0			0
$361$	−1.55098e6			−0.0329673
$362$	−2.82549e7	+	2.82549e7i	−0.595618	+	0.595618i
$363$	1.65008e7	+	1.65008e7i	0.344974	+	0.344974i
$364$			6.56369e6i			0.136096i
$365$		0			0
$366$	−5.61952e6			−0.114619
$367$	1.10433e7	−	1.10433e7i	0.223410	−	0.223410i	−0.586523	−	0.809933i	$-0.699504\pi$
$367$	1.10433e7	−	1.10433e7i	0.223410	−	0.223410i	0.809933	+	0.586523i	$0.199504\pi$
$368$	−3.12859e7	−	3.12859e7i	−0.627777	−	0.627777i
$369$			3.78338e7i			0.753010i
$370$		0			0
$371$	5.42744e6			0.106285
$372$	−2.82693e7	+	2.82693e7i	−0.549144	+	0.549144i
$373$	3.15257e7	+	3.15257e7i	0.607489	+	0.607489i	0.942289	−	0.334800i	$-0.108669\pi$
$373$	3.15257e7	+	3.15257e7i	0.607489	+	0.607489i	−0.334800	+	0.942289i	$0.608669\pi$
$374$		−	4.58771e7i		−	0.876963i
$375$		0			0
$376$	3.82783e7			0.720095
$377$	−1.21037e7	+	1.21037e7i	−0.225888	+	0.225888i
$378$	−1.71918e7	−	1.71918e7i	−0.318308	−	0.318308i
$379$		−	7.24769e7i		−	1.33132i	−0.746256	−	0.665659i	$-0.768150\pi$
$379$		−	7.24769e7i		−	1.33132i	0.746256	−	0.665659i	$-0.231850\pi$
$380$		0			0
$381$	5.21894e7			0.943642
$382$	−1.95219e7	+	1.95219e7i	−0.350213	+	0.350213i
$383$	−5.97718e7	−	5.97718e7i	−1.06390	−	1.06390i	−0.997814	−	0.0660833i	$-0.978950\pi$
$383$	−5.97718e7	−	5.97718e7i	−1.06390	−	1.06390i	−0.0660833	−	0.997814i	$-0.521050\pi$
$384$			7.92520e7i			1.39964i
$385$		0			0
$386$	−6.16640e6			−0.107218
$387$	8.98819e6	−	8.98819e6i	0.155074	−	0.155074i
$388$	−7.23355e6	−	7.23355e6i	−0.123839	−	0.123839i
$389$			5.28956e7i			0.898608i	0.893379	+	0.449304i	$0.148328\pi$
$389$			5.28956e7i			0.898608i	−0.893379	+	0.449304i	$0.851672\pi$
$390$		0			0
$391$	7.18221e7			1.20151
$392$	5.92492e7	−	5.92492e7i	0.983613	−	0.983613i
$393$	4.50454e7	+	4.50454e7i	0.742117	+	0.742117i
$394$			9.99321e7i			1.63387i
$395$		0			0
$396$	−2.91043e7			−0.468675
$397$	4.84200e7	−	4.84200e7i	0.773844	−	0.773844i	−0.204933	−	0.978776i	$-0.565697\pi$
$397$	4.84200e7	−	4.84200e7i	0.773844	−	0.773844i	0.978776	+	0.204933i	$0.0656975\pi$
$398$	8.88791e7	+	8.88791e7i	1.40978	+	1.40978i
$399$		−	1.21072e7i		−	0.190601i
$400$		0			0
$401$	2.84505e7			0.441222			0.220611	−	0.975362i	$-0.429195\pi$
$401$	2.84505e7			0.441222			0.220611	+	0.975362i	$0.429195\pi$
$402$	−6.38859e7	+	6.38859e7i	−0.983392	+	0.983392i
$403$	7.43323e6	+	7.43323e6i	0.113570	+	0.113570i
$404$			1.09111e7i			0.165471i
$405$		0			0
$406$	−3.00433e7			−0.448921
$407$	−1.35212e7	+	1.35212e7i	−0.200554	+	0.200554i
$408$	4.67378e7	+	4.67378e7i	0.688157	+	0.688157i
$409$			1.04600e7i			0.152883i	0.997074	+	0.0764416i	$0.0243559\pi$
$409$			1.04600e7i			0.152883i	−0.997074	+	0.0764416i	$0.975644\pi$
$410$		0			0
$411$	−3.46765e6			−0.0499471
$412$	−7.62431e7	+	7.62431e7i	−1.09021	+	1.09021i
$413$	311381.	+	311381.i	0.00442020	+	0.00442020i
$414$		−	6.98873e7i		−	0.984912i
$415$		0			0
$416$	8.57799e6			0.119153
$417$	3.24984e7	−	3.24984e7i	0.448181	−	0.448181i
$418$	−5.34961e7	−	5.34961e7i	−0.732476	−	0.732476i
$419$		−	4.91256e7i		−	0.667829i	−0.942603	−	0.333915i	$-0.891630\pi$
$419$		−	4.91256e7i		−	0.667829i	0.942603	−	0.333915i	$-0.108370\pi$
$420$		0			0
$421$	−6.96342e7			−0.933203			−0.466601	−	0.884468i	$-0.654522\pi$
$421$	−6.96342e7			−0.933203			−0.466601	+	0.884468i	$0.654522\pi$
$422$	1.08830e8	−	1.08830e8i	1.44814	−	1.44814i
$423$	1.08337e7	+	1.08337e7i	0.143138	+	0.143138i
$424$			4.88625e7i			0.641030i
$425$		0			0
$426$	−1.31800e8			−1.70485
$427$	−1.19559e6	+	1.19559e6i	−0.0153568	+	0.0153568i
$428$	−3.32903e7	−	3.32903e7i	−0.424607	−	0.424607i
$429$		−	1.07388e7i		−	0.136015i
$430$		0			0
$431$	6.41393e7			0.801110			0.400555	−	0.916273i	$-0.368817\pi$
$431$	6.41393e7			0.801110			0.400555	+	0.916273i	$0.368817\pi$
$432$	3.92200e7	−	3.92200e7i	0.486471	−	0.486471i
$433$	−4.66215e7	−	4.66215e7i	−0.574278	−	0.574278i	0.359043	−	0.933321i	$-0.383103\pi$
$433$	−4.66215e7	−	4.66215e7i	−0.574278	−	0.574278i	−0.933321	+	0.359043i	$0.883103\pi$
$434$			1.84505e7i			0.225704i
$435$		0			0
$436$	1.17611e8			1.41903
$437$	8.37500e7	−	8.37500e7i	1.00355	−	1.00355i
$438$	−6.78696e6	−	6.78696e6i	−0.0807705	−	0.0807705i
$439$		−	1.03597e8i		−	1.22448i	−0.790670	−	0.612242i	$-0.790268\pi$
$439$		−	1.03597e8i		−	1.22448i	0.790670	−	0.612242i	$-0.209732\pi$
$440$		0			0
$441$	3.35379e7			0.391039
$442$	2.63628e7	−	2.63628e7i	0.305298	−	0.305298i
$443$	6.41399e7	+	6.41399e7i	0.737764	+	0.737764i	0.972145	−	0.234381i	$-0.0753063\pi$
$443$	6.41399e7	+	6.41399e7i	0.737764	+	0.737764i	−0.234381	+	0.972145i	$0.575306\pi$
$444$		−	5.90985e7i		−	0.675193i
$445$		0			0
$446$	4.27059e7			0.481375
$447$	−2.26164e7	+	2.26164e7i	−0.253222	+	0.253222i
$448$	2.05667e7	+	2.05667e7i	0.228733	+	0.228733i
$449$			1.35473e8i			1.49663i	0.663343	+	0.748315i	$0.269137\pi$
$449$			1.35473e8i			1.49663i	−0.663343	+	0.748315i	$0.730863\pi$
$450$		0			0
$451$	−9.98182e7			−1.08813
$452$	−1.73411e8	+	1.73411e8i	−1.87785	+	1.87785i
$453$	−9.15019e7	−	9.15019e7i	−0.984318	−	0.984318i
$454$		−	2.57742e6i		−	0.0275434i
$455$		0			0
$456$	1.09000e8			1.14956
$457$	−1.08878e8	+	1.08878e8i	−1.14075	+	1.14075i	−0.152440	+	0.988313i	$0.548713\pi$
$457$	−1.08878e8	+	1.08878e8i	−1.14075	+	1.14075i	−0.988313	+	0.152440i	$0.951287\pi$
$458$	1.56971e8	+	1.56971e8i	1.63389	+	1.63389i
$459$			9.00362e7i			0.931063i
$460$		0			0
$461$	−5.72952e7			−0.584811			−0.292405	−	0.956294i	$-0.594456\pi$
$461$	−5.72952e7			−0.584811			−0.292405	+	0.956294i	$0.594456\pi$
$462$	1.33278e7	−	1.33278e7i	0.135155	−	0.135155i
$463$	−8.86294e7	−	8.86294e7i	−0.892965	−	0.892965i	0.101836	−	0.994801i	$-0.467528\pi$
$463$	−8.86294e7	−	8.86294e7i	−0.892965	−	0.892965i	−0.994801	+	0.101836i	$0.967528\pi$
$464$		−	6.85384e7i		−	0.686088i
$465$		0			0
$466$	−2.16659e8			−2.14101
$467$	−6.73039e7	+	6.73039e7i	−0.660830	+	0.660830i	−0.955576	−	0.294746i	$-0.904765\pi$
$467$	−6.73039e7	+	6.73039e7i	−0.660830	+	0.660830i	0.294746	+	0.955576i	$0.404765\pi$
$468$	−1.67245e7	−	1.67245e7i	−0.163161	−	0.163161i
$469$			2.71844e7i			0.263512i
$470$		0			0
$471$	1.23866e8			1.18546
$472$	−2.80332e6	+	2.80332e6i	−0.0266592	+	0.0266592i
$473$	2.37139e7	+	2.37139e7i	0.224088	+	0.224088i
$474$		−	1.33403e8i		−	1.25265i
$475$		0			0
$476$	4.26622e7			0.395569
$477$	−1.38293e7	+	1.38293e7i	−0.127422	+	0.127422i
$478$	−1.83116e8	−	1.83116e8i	−1.67665	−	1.67665i
$479$			6.12787e7i			0.557575i	0.960353	+	0.278787i	$0.0899324\pi$
$479$			6.12787e7i			0.557575i	−0.960353	+	0.278787i	$0.910068\pi$
$480$		0			0
$481$	−1.55396e7			−0.139638
$482$	−1.61819e7	+	1.61819e7i	−0.144507	+	0.144507i
$483$	2.08651e7	+	2.08651e7i	0.185173	+	0.185173i
$484$			1.35601e8i			1.19598i
$485$		0			0
$486$	1.49478e8			1.30217
$487$	1.31243e8	−	1.31243e8i	1.13629	−	1.13629i	0.147184	−	0.989109i	$-0.452979\pi$
$487$	1.31243e8	−	1.31243e8i	1.13629	−	1.13629i	0.989109	−	0.147184i	$-0.0470210\pi$
$488$	−1.07638e7	−	1.07638e7i	−0.0926200	−	0.0926200i
$489$		−	1.45689e8i		−	1.24595i
$490$		0			0
$491$	−2.31192e8			−1.95312			−0.976561	−	0.215243i	$-0.930946\pi$
$491$	−2.31192e8			−1.95312			−0.976561	+	0.215243i	$0.930946\pi$
$492$	2.18144e8	−	2.18144e8i	1.83167	−	1.83167i
$493$	7.86706e7	+	7.86706e7i	0.656556	+	0.656556i
$494$		−	6.14820e7i		−	0.509996i
$495$		0			0
$496$	−4.20914e7			−0.344944
$497$	−2.80414e7	+	2.80414e7i	−0.228418	+	0.228418i
$498$	−8.29889e7	−	8.29889e7i	−0.671943	−	0.671943i
$499$			5.98790e7i			0.481918i	0.970535	+	0.240959i	$0.0774619\pi$
$499$			5.98790e7i			0.481918i	−0.970535	+	0.240959i	$0.922538\pi$
$500$		0			0
$501$	−6.14662e7			−0.488791
$502$	8.50019e6	−	8.50019e6i	0.0671920	−	0.0671920i
$503$	−1.01711e8	−	1.01711e8i	−0.799215	−	0.799215i	0.183757	−	0.982972i	$-0.441174\pi$
$503$	−1.01711e8	−	1.01711e8i	−0.799215	−	0.799215i	−0.982972	+	0.183757i	$0.941174\pi$
$504$		−	1.93519e7i		−	0.151158i
$505$		0			0
$506$	1.84386e8			1.42324
$507$	−6.42460e7	+	6.42460e7i	−0.492972	+	0.492972i
$508$	2.14441e8	+	2.14441e8i	1.63575	+	1.63575i
$509$		−	2.18642e8i		−	1.65798i	−0.559261	−	0.828992i	$-0.688915\pi$
$509$		−	2.18642e8i		−	1.65798i	0.559261	−	0.828992i	$-0.311085\pi$
$510$		0			0
$511$	−2.88795e6			−0.0216435
$512$	−1.13601e8	+	1.13601e8i	−0.846396	+	0.846396i
$513$	1.04989e8	+	1.04989e8i	0.777663	+	0.777663i
$514$		−	1.63481e8i		−	1.20387i
$515$		0			0
$516$	−1.03649e8			−0.754425
$517$	−2.85830e7	+	2.85830e7i	−0.206840	+	0.206840i
$518$	−1.92859e7	−	1.92859e7i	−0.138756	−	0.138756i
$519$			5.75727e7i			0.411827i
$520$		0			0
$521$	7.37986e7			0.521837			0.260919	−	0.965361i	$-0.415975\pi$
$521$	7.37986e7			0.521837			0.260919	+	0.965361i	$0.415975\pi$
$522$	7.65514e7	−	7.65514e7i	0.538197	−	0.538197i
$523$	1.14081e8	+	1.14081e8i	0.797461	+	0.797461i	0.982695	−	0.185233i	$-0.0593041\pi$
$523$	1.14081e8	+	1.14081e8i	0.797461	+	0.797461i	−0.185233	+	0.982695i	$0.559304\pi$
$524$			3.70174e8i			2.57283i
$525$		0			0
$526$	1.76990e8			1.21616
$527$	4.83139e7	−	4.83139e7i	0.330096	−	0.330096i
$528$	3.04049e7	+	3.04049e7i	0.206558	+	0.206558i
$529$			1.40627e8i			0.949952i
$530$		0			0
$531$	−1.58682e6			−0.0105985
$532$	4.97473e7	−	4.97473e7i	0.330396	−	0.330396i
$533$	−5.73595e7	−	5.73595e7i	−0.378812	−	0.378812i
$534$			2.33417e8i			1.53288i
$535$		0			0
$536$	−2.44737e8			−1.58930
$537$	2.69523e7	−	2.69523e7i	0.174050	−	0.174050i
$538$	−4.25884e7	−	4.25884e7i	−0.273492	−	0.273492i
$539$			8.84843e7i			0.565067i
$540$		0			0
$541$	1.79424e8			1.13315			0.566575	−	0.824010i	$-0.308268\pi$
$541$	1.79424e8			1.13315			0.566575	+	0.824010i	$0.308268\pi$
$542$	5.26176e7	−	5.26176e7i	0.330471	−	0.330471i
$543$	4.29883e7	+	4.29883e7i	0.268504	+	0.268504i
$544$		−	5.57545e7i		−	0.346325i
$545$		0			0
$546$	1.53173e7			0.0941034
$547$	1.02489e7	−	1.02489e7i	0.0626205	−	0.0626205i	−0.675103	−	0.737723i	$-0.735901\pi$
$547$	1.02489e7	−	1.02489e7i	0.0626205	−	0.0626205i	0.737723	+	0.675103i	$0.235901\pi$
$548$	−1.42482e7	−	1.42482e7i	−0.0865805	−	0.0865805i
$549$		−	6.09282e6i		−	0.0368215i
$550$		0			0
$551$	1.83472e8			1.09677
$552$	−1.87846e8	+	1.87846e8i	−1.11682	+	1.11682i
$553$	−2.83824e7	−	2.83824e7i	−0.167832	−	0.167832i
$554$		−	1.98400e8i		−	1.16684i
$555$		0			0
$556$	2.67065e8			1.55379
$557$	−2.01202e8	+	2.01202e8i	−1.16430	+	1.16430i	−0.180781	+	0.983523i	$0.557863\pi$
$557$	−2.01202e8	+	2.01202e8i	−1.16430	+	1.16430i	−0.983523	+	0.180781i	$0.942137\pi$
$558$	−4.70124e7	−	4.70124e7i	−0.270589	−	0.270589i
$559$			2.72539e7i			0.156024i
$560$		0			0
$561$	−6.97995e7			−0.395334
$562$	1.01914e8	−	1.01914e8i	0.574151	−	0.574151i
$563$	1.36525e8	+	1.36525e8i	0.765045	+	0.765045i	0.977230	−	0.212185i	$-0.0680579\pi$
$563$	1.36525e8	+	1.36525e8i	0.765045	+	0.765045i	−0.212185	+	0.977230i	$0.568058\pi$
$564$		−	1.24931e8i		−	0.696358i
$565$		0			0
$566$	−5.13674e8			−2.83295
$567$	−1.29937e7	+	1.29937e7i	−0.0712826	+	0.0712826i
$568$	−2.52453e8	−	2.52453e8i	−1.37764	−	1.37764i
$569$		−	1.51174e8i		−	0.820616i	−0.911947	−	0.410308i	$-0.865421\pi$
$569$		−	1.51174e8i		−	0.820616i	0.911947	−	0.410308i	$-0.134579\pi$
$570$		0			0
$571$	−1.50325e8			−0.807462			−0.403731	−	0.914878i	$-0.632287\pi$
$571$	−1.50325e8			−0.807462			−0.403731	+	0.914878i	$0.632287\pi$
$572$	4.41249e7	−	4.41249e7i	0.235774	−	0.235774i
$573$	2.97015e7	+	2.97015e7i	0.157876	+	0.157876i
$574$		−	1.42376e8i		−	0.752835i
$575$		0			0
$576$	−1.04809e8			−0.548442
$577$	2.48351e7	−	2.48351e7i	0.129282	−	0.129282i	−0.639505	−	0.768787i	$-0.720861\pi$
$577$	2.48351e7	−	2.48351e7i	0.129282	−	0.129282i	0.768787	+	0.639505i	$0.220861\pi$
$578$	6.00977e7	+	6.00977e7i	0.311225	+	0.311225i
$579$			9.38184e6i			0.0483339i
$580$		0			0
$581$	−3.53130e7			−0.180055
$582$	−1.68805e7	+	1.68805e7i	−0.0856283	+	0.0856283i
$583$	−3.64863e7	−	3.64863e7i	−0.184130	−	0.184130i
$584$		−	2.59998e7i		−	0.130536i
$585$		0			0
$586$	1.68084e8			0.835285
$587$	−1.89183e7	+	1.89183e7i	−0.0935337	+	0.0935337i	−0.752325	−	0.658792i	$-0.771068\pi$
$587$	−1.89183e7	+	1.89183e7i	−0.0935337	+	0.0935337i	0.658792	+	0.752325i	$0.271068\pi$
$588$	−1.93374e8	−	1.93374e8i	−0.951190	−	0.951190i
$589$		−	1.12675e8i		−	0.551420i
$590$		0			0
$591$	1.52041e8			0.736544
$592$	4.39972e7	−	4.39972e7i	0.212061	−	0.212061i
$593$	−6.70320e7	−	6.70320e7i	−0.321453	−	0.321453i	0.527871	−	0.849324i	$-0.322990\pi$
$593$	−6.70320e7	−	6.70320e7i	−0.321453	−	0.321453i	−0.849324	+	0.527871i	$0.822990\pi$
$594$			2.31147e8i			1.10288i
$595$		0			0
$596$	−1.85857e8			−0.877892
$597$	1.35225e8	−	1.35225e8i	0.635525	−	0.635525i
$598$	1.05956e8	+	1.05956e8i	0.495474	+	0.495474i
$599$		−	2.44898e7i		−	0.113947i	−0.998376	−	0.0569737i	$-0.981855\pi$
$599$		−	2.44898e7i		−	0.113947i	0.998376	−	0.0569737i	$-0.0181451\pi$
$600$		0			0
$601$	4.81673e7			0.221886			0.110943	−	0.993827i	$-0.464613\pi$
$601$	4.81673e7			0.221886			0.110943	+	0.993827i	$0.464613\pi$
$602$	−3.38243e7	+	3.38243e7i	−0.155038	+	0.155038i
$603$	−6.92666e7	−	6.92666e7i	−0.315916	−	0.315916i
$604$		−	7.51944e8i		−	3.41252i
$605$		0			0
$606$	2.54625e7			0.114415
$607$	1.57626e8	−	1.57626e8i	0.704792	−	0.704792i	−0.260643	−	0.965435i	$-0.583935\pi$
$607$	1.57626e8	−	1.57626e8i	0.704792	−	0.704792i	0.965435	+	0.260643i	$0.0839347\pi$
$608$	−6.50140e7	−	6.50140e7i	−0.289265	−	0.289265i
$609$			4.57093e7i			0.202373i
$610$		0			0
$611$	−3.28498e7			−0.144015
$612$	−1.08705e8	+	1.08705e8i	−0.474235	+	0.474235i
$613$	−1.99141e8	−	1.99141e8i	−0.864528	−	0.864528i	0.127332	−	0.991860i	$-0.459359\pi$
$613$	−1.99141e8	−	1.99141e8i	−0.864528	−	0.864528i	−0.991860	+	0.127332i	$0.959359\pi$
$614$			5.64968e8i			2.44073i
$615$		0			0
$616$	5.10568e7			0.218429
$617$	2.14639e7	−	2.14639e7i	0.0913805	−	0.0913805i	−0.659939	−	0.751319i	$-0.729418\pi$
$617$	2.14639e7	−	2.14639e7i	0.0913805	−	0.0913805i	0.751319	+	0.659939i	$0.229418\pi$
$618$	1.77925e8	+	1.77925e8i	0.753825	+	0.753825i
$619$			1.51441e8i			0.638514i	0.947668	+	0.319257i	$0.103433\pi$
$619$			1.51441e8i			0.638514i	−0.947668	+	0.319257i	$0.896567\pi$
$620$		0			0
$621$	−3.61868e8			−1.51104
$622$	−5.05859e8	+	5.05859e8i	−2.10212	+	2.10212i
$623$	4.96611e7	+	4.96611e7i	0.205377	+	0.205377i
$624$			3.49437e7i			0.143819i
$625$		0			0
$626$	6.63314e8			2.70394
$627$	−8.13915e7	+	8.13915e7i	−0.330199	+	0.330199i
$628$	5.08952e8	+	5.08952e8i	2.05493	+	2.05493i
$629$			1.01003e8i			0.405865i
$630$		0			0
$631$	5.35161e7			0.213008			0.106504	−	0.994312i	$-0.466034\pi$
$631$	5.35161e7			0.213008			0.106504	+	0.994312i	$0.466034\pi$
$632$	2.55523e8	−	2.55523e8i	1.01223	−	1.01223i
$633$	−1.65579e8	−	1.65579e8i	−0.652820	−	0.652820i
$634$			7.15735e8i			2.80856i
$635$		0			0
$636$	1.59475e8			0.619900
$637$	−5.08466e7	+	5.08466e7i	−0.196718	+	0.196718i
$638$	2.01968e8	+	2.01968e8i	0.777716	+	0.777716i
$639$		−	1.42901e8i		−	0.547686i
$640$		0			0
$641$	−7.32342e7			−0.278061			−0.139030	−	0.990288i	$-0.544399\pi$
$641$	−7.32342e7			−0.278061			−0.139030	+	0.990288i	$0.544399\pi$
$642$	−7.76879e7	+	7.76879e7i	−0.293595	+	0.293595i
$643$	2.96289e8	+	2.96289e8i	1.11450	+	1.11450i	0.992534	+	0.121971i	$0.0389215\pi$
$643$	2.96289e8	+	2.96289e8i	1.11450	+	1.11450i	0.121971	+	0.992534i	$0.461078\pi$
$644$			1.71465e8i			0.641975i
$645$		0			0
$646$	−3.99616e8			−1.48233
$647$	1.72144e8	−	1.72144e8i	0.635592	−	0.635592i	−0.313873	−	0.949465i	$-0.601627\pi$
$647$	1.72144e8	−	1.72144e8i	0.635592	−	0.635592i	0.949465	+	0.313873i	$0.101627\pi$
$648$	−1.16981e8	−	1.16981e8i	−0.429921	−	0.429921i
$649$		−	4.18656e6i		−	0.0153152i
$650$		0			0
$651$	2.80714e7			0.101747
$652$	5.98622e8	−	5.98622e8i	2.15978	−	2.15978i
$653$	−8.72104e7	−	8.72104e7i	−0.313205	−	0.313205i	0.532945	−	0.846150i	$-0.321085\pi$
$653$	−8.72104e7	−	8.72104e7i	−0.313205	−	0.313205i	−0.846150	+	0.532945i	$0.821085\pi$
$654$		−	2.74464e8i		−	0.981187i
$655$		0			0
$656$	3.24804e8			1.15056
$657$	7.35858e6	−	7.35858e6i	0.0259477	−	0.0259477i
$658$	−4.07693e7	−	4.07693e7i	−0.143105	−	0.143105i
$659$		−	7.70809e7i		−	0.269334i	−0.990891	−	0.134667i	$-0.957004\pi$
$659$		−	7.70809e7i		−	0.269334i	0.990891	−	0.134667i	$-0.0429964\pi$
$660$		0			0
$661$	8.33416e7			0.288574			0.144287	−	0.989536i	$-0.453911\pi$
$661$	8.33416e7			0.288574			0.144287	+	0.989536i	$0.453911\pi$
$662$	−1.64992e8	+	1.64992e8i	−0.568709	+	0.568709i
$663$	−4.01096e7	−	4.01096e7i	−0.137628	−	0.137628i
$664$		−	3.17918e8i		−	1.08595i
$665$		0			0
$666$	9.82821e7			0.332699
$667$	−3.16188e8	+	3.16188e8i	−1.06554	+	1.06554i
$668$	−2.52559e8	−	2.52559e8i	−0.847291	−	0.847291i
$669$		−	6.49747e7i		−	0.217003i
$670$		0			0
$671$	1.60749e7			0.0532085
$672$	1.61973e7	−	1.61973e7i	0.0533746	−	0.0533746i
$673$	−2.38317e8	−	2.38317e8i	−0.781827	−	0.781827i	0.198312	−	0.980139i	$-0.436454\pi$
$673$	−2.38317e8	−	2.38317e8i	−0.781827	−	0.781827i	−0.980139	+	0.198312i	$0.936454\pi$
$674$		−	7.37223e8i		−	2.40779i
$675$		0			0
$676$	−5.27961e8			−1.70908
$677$	3.21631e8	−	3.21631e8i	1.03655	−	1.03655i	0.0372467	−	0.999306i	$-0.488141\pi$
$677$	3.21631e8	−	3.21631e8i	1.03655	−	1.03655i	0.999306	−	0.0372467i	$-0.0118587\pi$
$678$	4.04680e8	+	4.04680e8i	1.29844	+	1.29844i
$679$			7.18291e6i			0.0229452i
$680$		0			0
$681$	−3.92141e6			−0.0124165
$682$	1.24035e8	−	1.24035e8i	0.391012	−	0.391012i
$683$	−9.24444e7	−	9.24444e7i	−0.290147	−	0.290147i	0.546991	−	0.837138i	$-0.315773\pi$
$683$	−9.24444e7	−	9.24444e7i	−0.290147	−	0.290147i	−0.837138	+	0.546991i	$0.815773\pi$
$684$			2.53515e8i			0.792202i
$685$		0			0
$686$	−2.60508e8			−0.806954
$687$	2.38823e8	−	2.38823e8i	0.736556	−	0.736556i
$688$	−7.71638e7	−	7.71638e7i	−0.236945	−	0.236945i
$689$		−	4.19329e7i		−	0.128203i
$690$		0			0
$691$	3.46205e8			1.04930			0.524649	−	0.851319i	$-0.324197\pi$
$691$	3.46205e8			1.04930			0.524649	+	0.851319i	$0.324197\pi$
$692$	−2.36561e8	+	2.36561e8i	−0.713878	+	0.713878i
$693$	1.44503e7	+	1.44503e7i	0.0434188	+	0.0434188i
$694$			4.63899e8i			1.38786i
$695$		0			0
$696$	−4.11515e8			−1.22056
$697$	−3.72821e8	+	3.72821e8i	−1.10104	+	1.10104i
$698$	−3.14554e8	−	3.14554e8i	−0.924974	−	0.924974i
$699$			3.29635e8i			0.965165i
$700$		0			0
$701$	1.14851e8			0.333413			0.166706	−	0.986007i	$-0.446687\pi$
$701$	1.14851e8			0.333413			0.166706	+	0.986007i	$0.446687\pi$
$702$	−1.32826e8	+	1.32826e8i	−0.383947	+	0.383947i
$703$	1.17777e8	+	1.17777e8i	0.338996	+	0.338996i
$704$		−	2.76521e8i		−	0.792521i
$705$		0			0
$706$	−4.05964e8			−1.15365
$707$	5.41734e6	−	5.41734e6i	0.0153295	−	0.0153295i
$708$	9.14934e6	+	9.14934e6i	0.0257804	+	0.0257804i
$709$			1.57973e8i			0.443245i	0.975133	+	0.221623i	$0.0711353\pi$
$709$			1.57973e8i			0.443245i	−0.975133	+	0.221623i	$0.928865\pi$
$710$		0			0
$711$	1.44639e8			0.402416
$712$	−4.47092e8	+	4.47092e8i	−1.23867	+	1.23867i
$713$	1.94180e8	+	1.94180e8i	0.535718	+	0.535718i
$714$		−	9.95584e7i		−	0.273516i
$715$		0			0
$716$	2.21489e8			0.603410
$717$	−2.78601e8	+	2.78601e8i	−0.755832	+	0.755832i
$718$	−5.73532e8	−	5.73532e8i	−1.54947	−	1.54947i
$719$		−	2.04633e8i		−	0.550540i	−0.961367	−	0.275270i	$-0.911233\pi$
$719$		−	2.04633e8i		−	0.550540i	0.961367	−	0.275270i	$-0.0887672\pi$
$720$		0			0
$721$	7.57095e7			0.201997
$722$	−1.48719e7	+	1.48719e7i	−0.0395143	+	0.0395143i
$723$	2.46199e7	+	2.46199e7i	0.0651437	+	0.0651437i
$724$			3.53269e8i			0.930872i
$725$		0			0
$726$	3.16444e8			0.826964
$727$	4.71448e8	−	4.71448e8i	1.22696	−	1.22696i	0.261854	−	0.965108i	$-0.415666\pi$
$727$	4.71448e8	−	4.71448e8i	1.22696	−	1.22696i	0.965108	−	0.261854i	$-0.0843338\pi$
$728$	2.93392e7	+	2.93392e7i	0.0760422	+	0.0760422i
$729$		−	3.86559e8i		−	0.997776i
$730$		0			0
$731$	1.77142e8			0.453493
$732$	−3.51302e7	+	3.51302e7i	−0.0895670	+	0.0895670i
$733$	2.39548e8	+	2.39548e8i	0.608247	+	0.608247i	0.942488	−	0.334241i	$-0.108480\pi$
$733$	2.39548e8	+	2.39548e8i	0.608247	+	0.608247i	−0.334241	+	0.942488i	$0.608480\pi$
$734$		−	2.11783e8i		−	0.535553i
$735$		0			0
$736$	2.24085e8			0.562056
$737$	1.82749e8	−	1.82749e8i	0.456512	−	0.456512i
$738$	3.62778e8	+	3.62778e8i	0.902550	+	0.902550i
$739$		−	9.40080e7i		−	0.232933i	−0.993195	−	0.116467i	$-0.962843\pi$
$739$		−	9.40080e7i		−	0.232933i	0.993195	−	0.116467i	$-0.0371568\pi$
$740$		0			0
$741$	−9.35415e7			−0.229906
$742$	5.20422e7	−	5.20422e7i	0.127393	−	0.127393i
$743$	2.43455e8	+	2.43455e8i	0.593542	+	0.593542i	0.938586	−	0.345044i	$-0.112136\pi$
$743$	2.43455e8	+	2.43455e8i	0.593542	+	0.593542i	−0.345044	+	0.938586i	$0.612136\pi$
$744$			2.52723e8i			0.613658i
$745$		0			0
$746$	6.04583e8			1.45626
$747$	8.99786e7	−	8.99786e7i	0.215863	−	0.215863i
$748$	−2.86799e8	−	2.86799e8i	−0.685288	−	0.685288i
$749$			3.30573e7i			0.0786724i
$750$		0			0
$751$	−2.93143e8			−0.692085			−0.346042	−	0.938219i	$-0.612475\pi$
$751$	−2.93143e8			−0.692085			−0.346042	+	0.938219i	$0.612475\pi$
$752$	9.30076e7	−	9.30076e7i	0.218708	−	0.218708i
$753$	−1.29326e7	−	1.29326e7i	−0.0302901	−	0.0302901i
$754$			2.32118e8i			0.541495i
$755$		0			0
$756$	−2.14949e8			−0.497473
$757$	−3.79029e8	+	3.79029e8i	−0.873746	+	0.873746i	−0.992878	−	0.119132i	$-0.961989\pi$
$757$	−3.79029e8	+	3.79029e8i	−0.873746	+	0.873746i	0.119132	+	0.992878i	$0.461989\pi$
$758$	−6.94961e8	−	6.94961e8i	−1.59571	−	1.59571i
$759$		−	2.80534e8i		−	0.641593i
$760$		0			0
$761$	−4.65585e8			−1.05644			−0.528221	−	0.849107i	$-0.677141\pi$
$761$	−4.65585e8			−1.05644			−0.528221	+	0.849107i	$0.677141\pi$
$762$	5.00430e8	−	5.00430e8i	1.13104	−	1.13104i
$763$	−5.83941e7	−	5.83941e7i	−0.131461	−	0.131461i
$764$			2.44081e8i			0.547336i
$765$		0			0
$766$	−1.14627e9			−2.55035
$767$	2.40576e6	−	2.40576e6i	0.00533171	−	0.00533171i
$768$	4.37322e8	+	4.37322e8i	0.965424	+	0.965424i
$769$		−	9.01841e7i		−	0.198313i	−0.995072	−	0.0991565i	$-0.968386\pi$
$769$		−	9.01841e7i		−	0.198313i	0.995072	−	0.0991565i	$-0.0316144\pi$
$770$		0			0
$771$	−2.48728e8			−0.542702
$772$	−3.85490e7	+	3.85490e7i	−0.0837841	+	0.0837841i
$773$	9.17018e7	+	9.17018e7i	0.198536	+	0.198536i	0.799372	−	0.600836i	$-0.205166\pi$
$773$	9.17018e7	+	9.17018e7i	0.198536	+	0.198536i	−0.600836	+	0.799372i	$0.705166\pi$
$774$		−	1.72371e8i		−	0.371741i
$775$		0			0
$776$	−6.46669e7			−0.138387
$777$	−2.93424e7	+	2.93424e7i	−0.0625508	+	0.0625508i
$778$	5.07201e8	+	5.07201e8i	1.07706	+	1.07706i
$779$			8.69474e8i			1.83926i
$780$		0			0
$781$	3.77020e8			0.791428
$782$	6.88682e8	−	6.88682e8i	1.44012	−	1.44012i
$783$	−3.96373e8	−	3.96373e8i	−0.825694	−	0.825694i
$784$		−	2.87924e8i		−	0.597488i
$785$		0			0
$786$	8.63855e8			1.77899
$787$	−5.51822e8	+	5.51822e8i	−1.13207	+	1.13207i	−0.142243	+	0.989832i	$0.545431\pi$
$787$	−5.51822e8	+	5.51822e8i	−1.13207	+	1.13207i	−0.989832	+	0.142243i	$0.954569\pi$
$788$	6.24722e8	+	6.24722e8i	1.27676	+	1.27676i
$789$		−	2.69281e8i		−	0.548245i
$790$		0			0
$791$	1.72197e8			0.347934
$792$	−1.30094e8	+	1.30094e8i	−0.261868	+	0.261868i
$793$	9.23728e6	+	9.23728e6i	0.0185236	+	0.0185236i
$794$		−	9.28572e8i		−	1.85504i
$795$		0			0
$796$	1.11125e9			2.20329
$797$	1.79500e8	−	1.79500e8i	0.354559	−	0.354559i	−0.507244	−	0.861803i	$-0.669336\pi$
$797$	1.79500e8	−	1.79500e8i	0.354559	−	0.354559i	0.861803	+	0.507244i	$0.169336\pi$
$798$	−1.16093e8	−	1.16093e8i	−0.228453	−	0.228453i
$799$			2.13514e8i			0.418588i
$800$		0			0
$801$	−2.53076e8			−0.492440
$802$	2.72804e8	−	2.72804e8i	0.528844	−	0.528844i
$803$	1.94144e7	+	1.94144e7i	0.0374954	+	0.0374954i
$804$			7.98761e8i			1.53691i
$805$		0			0
$806$	1.42550e8			0.272247
$807$	−6.47959e7	+	6.47959e7i	−0.123290	+	0.123290i
$808$	4.87716e7	+	4.87716e7i	0.0924556	+	0.0924556i
$809$			6.73245e7i			0.127153i	0.997977	+	0.0635766i	$0.0202507\pi$
$809$			6.73245e7i			0.127153i	−0.997977	+	0.0635766i	$0.979749\pi$
$810$		0			0
$811$	−6.32767e8			−1.18626			−0.593132	−	0.805105i	$-0.702109\pi$
$811$	−6.32767e8			−1.18626			−0.593132	+	0.805105i	$0.702109\pi$
$812$	−1.87815e8	+	1.87815e8i	−0.350802	+	0.350802i
$813$	−8.00548e7	−	8.00548e7i	−0.148976	−	0.148976i
$814$			2.59301e8i			0.480763i
$815$		0			0
$816$	2.27124e8			0.418016
$817$	2.06561e8	−	2.06561e8i	0.378777	−	0.378777i
$818$	1.00298e8	+	1.00298e8i	0.183244	+	0.183244i
$819$			1.66074e7i			0.0302309i
$820$		0			0
$821$	4.28302e8			0.773964			0.386982	−	0.922087i	$-0.373518\pi$
$821$	4.28302e8			0.773964			0.386982	+	0.922087i	$0.373518\pi$
$822$	−3.32504e7	+	3.32504e7i	−0.0598661	+	0.0598661i
$823$	−7.00816e7	−	7.00816e7i	−0.125720	−	0.125720i	0.641447	−	0.767167i	$-0.278334\pi$
$823$	−7.00816e7	−	7.00816e7i	−0.125720	−	0.125720i	−0.767167	+	0.641447i	$0.778334\pi$
$824$			6.81602e8i			1.21829i
$825$		0			0
$826$	5.97149e6			0.0105960
$827$	−6.05979e8	+	6.05979e8i	−1.07137	+	1.07137i	−0.0741255	+	0.997249i	$0.523617\pi$
$827$	−6.05979e8	+	6.05979e8i	−1.07137	+	1.07137i	−0.997249	+	0.0741255i	$0.976383\pi$
$828$	−4.36899e8	−	4.36899e8i	−0.769644	−	0.769644i
$829$			6.84492e8i			1.20145i	0.799456	+	0.600724i	$0.205121\pi$
$829$			6.84492e8i			1.20145i	−0.799456	+	0.600724i	$0.794879\pi$
$830$		0			0
$831$	−3.01854e8			−0.526011
$832$	1.58900e8	−	1.58900e8i	0.275902	−	0.275902i
$833$	3.30489e8	+	3.30489e8i	0.571770	+	0.571770i
$834$		−	6.23235e8i		−	1.07437i
$835$		0			0
$836$	−6.68859e8			−1.14476
$837$	−2.43424e8	+	2.43424e8i	−0.415133	+	0.415133i
$838$	−4.71051e8	−	4.71051e8i	−0.800454	−	0.800454i
$839$		−	4.58117e8i		−	0.775695i	−0.921724	−	0.387847i	$-0.873219\pi$
$839$		−	4.58117e8i		−	0.775695i	0.921724	−	0.387847i	$-0.126781\pi$
$840$		0			0
$841$	−9.78528e7			−0.164507
$842$	−6.67703e8	+	6.67703e8i	−1.11853	+	1.11853i
$843$	−1.55057e8	−	1.55057e8i	−0.258827	−	0.258827i
$844$		−	1.36069e9i		−	2.26325i
$845$		0			0
$846$	2.07763e8			0.343128
$847$	6.73257e7	−	6.73257e7i	0.110798	−	0.110798i
$848$	1.18725e8	+	1.18725e8i	0.194694	+	0.194694i
$849$			7.81528e8i			1.27709i
$850$		0			0
$851$	−4.05945e8			−0.658686
$852$	−8.23944e8	+	8.23944e8i	−1.33223	+	1.33223i
$853$	−1.74568e7	−	1.74568e7i	−0.0281267	−	0.0281267i	0.692904	−	0.721030i	$-0.256331\pi$
$853$	−1.74568e7	−	1.74568e7i	−0.0281267	−	0.0281267i	−0.721030	+	0.692904i	$0.756331\pi$
$854$			2.29284e7i			0.0368129i
$855$		0			0
$856$	−2.97611e8			−0.474490
$857$	5.06507e8	−	5.06507e8i	0.804717	−	0.804717i	−0.179112	−	0.983829i	$-0.557322\pi$
$857$	5.06507e8	−	5.06507e8i	0.804717	−	0.804717i	0.983829	+	0.179112i	$0.0573225\pi$
$858$	−1.02972e8	−	1.02972e8i	−0.163026	−	0.163026i
$859$		−	1.02651e9i		−	1.61952i	−0.586764	−	0.809758i	$-0.699598\pi$
$859$		−	1.02651e9i		−	1.61952i	0.586764	−	0.809758i	$-0.300402\pi$
$860$		0			0
$861$	−2.16617e8			−0.339377
$862$	6.15014e8	−	6.15014e8i	0.960203	−	0.960203i
$863$	−3.37658e8	−	3.37658e8i	−0.525345	−	0.525345i	0.393836	−	0.919181i	$-0.371148\pi$
$863$	−3.37658e8	−	3.37658e8i	−0.525345	−	0.525345i	−0.919181	+	0.393836i	$0.871148\pi$
$864$			2.80913e8i			0.435543i
$865$		0			0
$866$	−8.94081e8			−1.37665
$867$	9.14354e7	−	9.14354e7i	0.140300	−	0.140300i
$868$	1.15343e8	+	1.15343e8i	0.176372	+	0.176372i
$869$			3.81605e8i			0.581507i
$870$		0			0
$871$	2.10029e8			0.317852
$872$	5.25715e8	−	5.25715e8i	0.792868	−	0.792868i
$873$	−1.83023e7	−	1.83023e7i	−0.0275082	−	0.0275082i
$874$		−	1.60611e9i		−	2.40570i
$875$		0			0
$876$	−8.48569e7			−0.126234
$877$	4.08316e8	−	4.08316e8i	0.605338	−	0.605338i	−0.336386	−	0.941724i	$-0.609205\pi$
$877$	4.08316e8	−	4.08316e8i	0.605338	−	0.605338i	0.941724	+	0.336386i	$0.109205\pi$
$878$	−9.93362e8	−	9.93362e8i	−1.46765	−	1.46765i
$879$		−	2.55731e8i		−	0.376545i
$880$		0			0
$881$	6.30879e8			0.922610			0.461305	−	0.887242i	$-0.347381\pi$
$881$	6.30879e8			0.922610			0.461305	+	0.887242i	$0.347381\pi$
$882$	3.21586e8	−	3.21586e8i	0.468696	−	0.468696i
$883$	1.37438e7	+	1.37438e7i	0.0199630	+	0.0199630i	0.717018	−	0.697055i	$-0.245507\pi$
$883$	1.37438e7	+	1.37438e7i	0.0199630	+	0.0199630i	−0.697055	+	0.717018i	$0.745507\pi$
$884$		−	3.29612e8i		−	0.477141i
$885$		0			0
$886$	1.23004e9			1.76855
$887$	−3.78526e8	+	3.78526e8i	−0.542406	+	0.542406i	−0.924234	−	0.381827i	$-0.875295\pi$
$887$	−3.78526e8	+	3.78526e8i	−0.542406	+	0.542406i	0.381827	+	0.924234i	$0.375295\pi$
$888$	−2.64166e8	−	2.64166e8i	−0.377258	−	0.377258i
$889$		−	2.12940e8i		−	0.303076i
$890$		0			0
$891$	1.74702e8			0.246982
$892$	2.66975e8	−	2.66975e8i	0.376163	−	0.376163i
$893$	2.48974e8	+	2.48974e8i	0.349622	+	0.349622i
$894$			4.33726e8i			0.607019i
$895$		0			0
$896$	3.23359e8			0.449533
$897$	1.61206e8	−	1.61206e8i	0.223359	−	0.223359i
$898$	1.29902e9	+	1.29902e9i	1.79385	+	1.79385i
$899$			4.25392e8i			0.585478i
$900$		0			0
$901$	−2.72552e8			−0.372628
$902$	−9.57129e8	+	9.57129e8i	−1.30422	+	1.30422i
$903$	5.14618e7	+	5.14618e7i	0.0698910	+	0.0698910i
$904$			1.55027e9i			2.09847i
$905$		0			0
$906$	−1.75477e9			−2.35959
$907$	−8.38586e7	+	8.38586e7i	−0.112390	+	0.112390i	−0.761065	−	0.648676i	$-0.775323\pi$
$907$	−8.38586e7	+	8.38586e7i	−0.112390	+	0.112390i	0.648676	+	0.761065i	$0.275323\pi$
$908$	−1.61127e7	−	1.61127e7i	−0.0215234	−	0.0215234i
$909$			2.76071e7i			0.0367561i
$910$		0			0
$911$	−2.63279e8			−0.348226			−0.174113	−	0.984726i	$-0.555706\pi$
$911$	−2.63279e8			−0.348226			−0.174113	+	0.984726i	$0.555706\pi$
$912$	2.64844e8	−	2.64844e8i	0.349145	−	0.349145i
$913$	2.37394e8	+	2.37394e8i	0.311930	+	0.311930i
$914$			2.08800e9i			2.73459i
$915$		0			0
$916$	1.96260e9			2.55356
$917$	1.83791e8	−	1.83791e8i	0.238351	−	0.238351i
$918$	8.63332e8	+	8.63332e8i	1.11596	+	1.11596i
$919$			8.86087e7i			0.114164i	0.998369	+	0.0570821i	$0.0181797\pi$
$919$			8.86087e7i			0.114164i	−0.998369	+	0.0570821i	$0.981820\pi$
$920$		0			0
$921$	8.59569e8			1.10028
$922$	−5.49388e8	+	5.49388e8i	−0.700948	+	0.700948i
$923$	2.16651e8	+	2.16651e8i	0.275521	+	0.275521i
$924$		−	1.66636e8i		−	0.211229i
$925$		0			0
$926$	−1.69968e9			−2.14060
$927$	−1.92910e8	+	1.92910e8i	−0.242167	+	0.242167i
$928$	2.45453e8	+	2.45453e8i	0.307131	+	0.307131i
$929$		−	9.93524e8i		−	1.23917i	−0.784929	−	0.619586i	$-0.787301\pi$
$929$		−	9.93524e8i		−	1.23917i	0.784929	−	0.619586i	$-0.212699\pi$
$930$		0			0
$931$	7.70749e8			0.955133
$932$	−1.35444e9	+	1.35444e9i	−1.67306	+	1.67306i
$933$	7.69637e8	+	7.69637e8i	0.947635	+	0.947635i
$934$			1.29072e9i			1.58413i
$935$		0			0
$936$	−1.49515e8			−0.182329
$937$	4.21096e8	−	4.21096e8i	0.511873	−	0.511873i	−0.403227	−	0.915100i	$-0.632111\pi$
$937$	4.21096e8	−	4.21096e8i	0.511873	−	0.511873i	0.915100	+	0.403227i	$0.132111\pi$
$938$	2.60663e8	+	2.60663e8i	0.315843	+	0.315843i
$939$		−	1.00920e9i		−	1.21893i
$940$		0			0
$941$	1.18128e9			1.41770			0.708851	−	0.705359i	$-0.249214\pi$
$941$	1.18128e9			1.41770			0.708851	+	0.705359i	$0.249214\pi$
$942$	1.18771e9	−	1.18771e9i	1.42089	−	1.42089i
$943$	−1.49842e9	−	1.49842e9i	−1.78689	−	1.78689i
$944$			1.36229e7i			0.0161939i
$945$		0			0
$946$	4.54772e8			0.537180
$947$	3.67092e8	−	3.67092e8i	0.432240	−	0.432240i	−0.457149	−	0.889390i	$-0.651130\pi$
$947$	3.67092e8	−	3.67092e8i	0.432240	−	0.432240i	0.889390	+	0.457149i	$0.151130\pi$
$948$	−8.33963e8	−	8.33963e8i	−0.978863	−	0.978863i
$949$			2.23126e7i			0.0261067i
$950$		0			0
$951$	1.08895e9			1.26610
$952$	1.90697e8	−	1.90697e8i	0.221021	−	0.221021i
$953$	−5.44279e8	−	5.44279e8i	−0.628844	−	0.628844i	0.318933	−	0.947777i	$-0.396676\pi$
$953$	−5.44279e8	−	5.44279e8i	−0.628844	−	0.628844i	−0.947777	+	0.318933i	$0.896676\pi$
$954$			2.65210e8i			0.305454i
$955$		0			0
$956$	−2.28949e9			−2.62038
$957$	3.07284e8	−	3.07284e8i	0.350594	−	0.350594i
$958$	5.87584e8	+	5.87584e8i	0.668304	+	0.668304i
$959$			1.41485e7i			0.0160419i
$960$		0			0
$961$	−6.26258e8			−0.705640
$962$	−1.49005e8	+	1.49005e8i	−0.167369	+	0.167369i
$963$	−8.42311e7	−	8.42311e7i	−0.0943178	−	0.0943178i
$964$			2.02322e8i			0.225846i
$965$		0			0
$966$	4.00139e8			0.443894
$967$	1.01015e9	−	1.01015e9i	1.11714	−	1.11714i	0.124976	−	0.992160i	$-0.460115\pi$
$967$	1.01015e9	−	1.01015e9i	1.11714	−	1.11714i	0.992160	−	0.124976i	$-0.0398854\pi$
$968$	6.06125e8	+	6.06125e8i	0.668245	+	0.668245i
$969$			6.07994e8i			0.668233i
$970$		0			0
$971$	−1.69787e9			−1.85459			−0.927295	−	0.374332i	$-0.877872\pi$
$971$	−1.69787e9			−1.85459			−0.927295	+	0.374332i	$0.877872\pi$
$972$	9.34459e8	−	9.34459e8i	1.01756	−	1.01756i
$973$	−1.32598e8	−	1.32598e8i	−0.143945	−	0.143945i
$974$		−	2.51691e9i		−	2.72390i
$975$		0			0
$976$	−5.23070e7			−0.0562613
$977$	−2.14608e8	+	2.14608e8i	−0.230124	+	0.230124i	−0.812744	−	0.582620i	$-0.802027\pi$
$977$	−2.14608e8	+	2.14608e8i	−0.230124	+	0.230124i	0.582620	+	0.812744i	$0.302027\pi$
$978$	−1.39697e9	−	1.39697e9i	−1.49338	−	1.49338i
$979$		−	6.67699e8i		−	0.711595i
$980$		0			0
$981$	2.97580e8			0.315208
$982$	−2.21684e9	+	2.21684e9i	−2.34099	+	2.34099i
$983$	7.60474e8	+	7.60474e8i	0.800615	+	0.800615i	0.983192	−	0.182576i	$-0.0584437\pi$
$983$	7.60474e8	+	7.60474e8i	0.800615	+	0.800615i	−0.182576	+	0.983192i	$0.558444\pi$
$984$		−	1.95017e9i		−	2.04686i
$985$		0			0
$986$	1.50870e9			1.57388
$987$	−6.20282e7	+	6.20282e7i	−0.0645116	+	0.0645116i
$988$	−3.84353e8	−	3.84353e8i	−0.398528	−	0.398528i
$989$			7.11960e8i			0.735981i
$990$		0			0
$991$	5.74834e8			0.590638			0.295319	−	0.955399i	$-0.404574\pi$
$991$	5.74834e8			0.590638			0.295319	+	0.955399i	$0.404574\pi$
$992$	1.50740e8	−	1.50740e8i	0.154416	−	0.154416i
$993$	2.51027e8	+	2.51027e8i	0.256373	+	0.256373i
$994$			5.37762e8i			0.547559i
$995$		0			0
$996$	−1.03761e9			−1.05016
$997$	−4.89316e8	+	4.89316e8i	−0.493746	+	0.493746i	−0.909484	−	0.415738i	$-0.863523\pi$
$997$	−4.89316e8	+	4.89316e8i	−0.493746	+	0.493746i	0.415738	+	0.909484i	$0.363523\pi$
$998$	5.74163e8	+	5.74163e8i	0.577622	+	0.577622i
$999$		−	5.08892e8i		−	0.510422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.7.c.c.18.2		4
3.2	odd	2		225.7.g.c.118.1		4
5.2	odd	4	inner	25.7.c.c.7.2		4
5.3	odd	4		5.7.c.a.2.1	✓	4
5.4	even	2		5.7.c.a.3.1	yes	4
15.2	even	4		225.7.g.c.82.1		4
15.8	even	4		45.7.g.a.37.2		4
15.14	odd	2		45.7.g.a.28.2		4
20.3	even	4		80.7.p.b.17.1		4
20.19	odd	2		80.7.p.b.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.7.c.a.2.1	✓	4	5.3	odd	4
5.7.c.a.3.1	yes	4	5.4	even	2
25.7.c.c.7.2		4	5.2	odd	4	inner
25.7.c.c.18.2		4	1.1	even	1	trivial
45.7.g.a.28.2		4	15.14	odd	2
45.7.g.a.37.2		4	15.8	even	4
80.7.p.b.17.1		4	20.3	even	4
80.7.p.b.33.1		4	20.19	odd	2
225.7.g.c.82.1		4	15.2	even	4
225.7.g.c.118.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.58872 - 9.58872i) q^{2} +(-14.5887 - 14.5887i) q^{3} -119.887i q^{4} -279.774 q^{6} +(-59.5240 + 59.5240i) q^{7} +(-535.887 - 535.887i) q^{8} -303.338i q^{9} +O(q^{10})\)	\(q+(9.58872 - 9.58872i) q^{2} +(-14.5887 - 14.5887i) q^{3} -119.887i q^{4} -279.774 q^{6} +(-59.5240 + 59.5240i) q^{7} +(-535.887 - 535.887i) q^{8} -303.338i q^{9} +800.309 q^{11} +(-1749.00 + 1749.00i) q^{12} +(459.889 + 459.889i) q^{13} +1141.52i q^{14} -2604.17 q^{16} +(2989.15 - 2989.15i) q^{17} +(-2908.63 - 2908.63i) q^{18} -6971.14i q^{19} +1736.76 q^{21} +(7673.94 - 7673.94i) q^{22} +(12013.8 + 12013.8i) q^{23} +15635.8i q^{24} +8819.50 q^{26} +(-15060.5 + 15060.5i) q^{27} +(7136.17 + 7136.17i) q^{28} +26318.7i q^{29} +16163.1 q^{31} +(9326.16 - 9326.16i) q^{32} +(-11675.5 - 11675.5i) q^{33} -57324.3i q^{34} -36366.4 q^{36} +(-16894.9 + 16894.9i) q^{37} +(-66844.4 - 66844.4i) q^{38} -13418.4i q^{39} -124725. q^{41} +(16653.3 - 16653.3i) q^{42} +(29630.9 + 29630.9i) q^{43} -95946.8i q^{44} +230394. q^{46} +(-35714.9 + 35714.9i) q^{47} +(37991.5 + 37991.5i) q^{48} +110563. i q^{49} -87215.7 q^{51} +(55134.8 - 55134.8i) q^{52} +(-45590.3 - 45590.3i) q^{53} +288822. i q^{54} +63796.3 q^{56} +(-101700. + 101700. i) q^{57} +(252363. + 252363. i) q^{58} -5231.18i q^{59} +20085.9 q^{61} +(154983. - 154983. i) q^{62} +(18055.9 + 18055.9i) q^{63} -345518. i q^{64} -223906. q^{66} +(228348. - 228348. i) q^{67} +(-358361. - 358361. i) q^{68} -350532. i q^{69} +471094. q^{71} +(-162555. + 162555. i) q^{72} +(24258.7 + 24258.7i) q^{73} +324002. i q^{74} -835751. q^{76} +(-47637.6 + 47637.6i) q^{77} +(-128665. - 128665. i) q^{78} +476823. i q^{79} +218293. q^{81} +(-1.19595e6 + 1.19595e6i) q^{82} +(296628. + 296628. i) q^{83} -208215. i q^{84} +568245. q^{86} +(383957. - 383957. i) q^{87} +(-428875. - 428875. i) q^{88} -834303. i q^{89} -54748.9 q^{91} +(1.44030e6 - 1.44030e6i) q^{92} +(-235799. - 235799. i) q^{93} +684921. i q^{94} -272113. q^{96} +(60336.2 - 60336.2i) q^{97} +(1.06016e6 + 1.06016e6i) q^{98} -242764. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8}+O(q^{10}) \) 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8	\( 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8} - 1052 q^{11} - 3480 q^{12} - 1960 q^{13} - 776 q^{16} + 3280 q^{17} + 870 q^{18} + 3828 q^{21} + 27520 q^{22} + 39010 q^{23} + 44068 q^{26} - 31320 q^{27} + 4840 q^{28} - 33172 q^{31} + 48760 q^{32} - 22260 q^{33} - 40836 q^{36} - 146860 q^{37} - 218040 q^{38} - 213932 q^{41} + 31680 q^{42} + 72050 q^{43} + 323288 q^{46} - 830 q^{47} + 74160 q^{48} - 172212 q^{51} + 173300 q^{52} + 29620 q^{53} + 467280 q^{56} - 195840 q^{57} + 554640 q^{58} - 111052 q^{61} + 610520 q^{62} + 350130 q^{63} - 457824 q^{66} + 146930 q^{67} - 775780 q^{68} + 1310188 q^{71} - 899460 q^{72} - 553540 q^{73} - 2073840 q^{76} + 476300 q^{77} - 268200 q^{78} - 624816 q^{81} - 2554880 q^{82} - 536870 q^{83} + 1019128 q^{86} + 763440 q^{87} + 187680 q^{88} + 1131548 q^{91} + 2552680 q^{92} - 444660 q^{93} - 568992 q^{96} + 59420 q^{97} + 1892810 q^{98}+O(q^{100}) \) 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8 - 1052 * q^11 - 3480 * q^12 - 1960 * q^13 - 776 * q^16 + 3280 * q^17 + 870 * q^18 + 3828 * q^21 + 27520 * q^22 + 39010 * q^23 + 44068 * q^26 - 31320 * q^27 + 4840 * q^28 - 33172 * q^31 + 48760 * q^32 - 22260 * q^33 - 40836 * q^36 - 146860 * q^37 - 218040 * q^38 - 213932 * q^41 + 31680 * q^42 + 72050 * q^43 + 323288 * q^46 - 830 * q^47 + 74160 * q^48 - 172212 * q^51 + 173300 * q^52 + 29620 * q^53 + 467280 * q^56 - 195840 * q^57 + 554640 * q^58 - 111052 * q^61 + 610520 * q^62 + 350130 * q^63 - 457824 * q^66 + 146930 * q^67 - 775780 * q^68 + 1310188 * q^71 - 899460 * q^72 - 553540 * q^73 - 2073840 * q^76 + 476300 * q^77 - 268200 * q^78 - 624816 * q^81 - 2554880 * q^82 - 536870 * q^83 + 1019128 * q^86 + 763440 * q^87 + 187680 * q^88 + 1131548 * q^91 + 2552680 * q^92 - 444660 * q^93 - 568992 * q^96 + 59420 * q^97 + 1892810 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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